His three years with the Bills were special, filled with long-lasting memories.

His exit wasn't.

Traded to Cleveland in March for a third-round draft pick (No. 65 overall), Taylor said Tuesday that he holds no bitterness toward the Bills, but that the team's decision to part ways with him is fueling his desire to deliver for the Browns.

It's driving him.

"Each year has its own way of motivating itself," Taylor said. "But definitely how I think it ended there, it's motivation for this year."

Coming off a "perfect" performance in his preseason debut for the Browns last week, Taylor, who has quickly established himself as a leader in Cleveland, will face his former teammates for the first time Friday night when the Bills visit in the second exhibition for both teams.

Taylor made it clear that there's no resentment and that his focus this week, and every week, is on improving the Browns — not paying back the Bills.

"I'm looking forward to Week 2 of the preseason," Taylor said. "I'm not going to make this about me or Buffalo. It's an opportunity for us to get better as a team, an opportunity for me to get better as a player."

While that's honorable, Taylor reiterated that if somewhere down the line the Browns and Bills ever matched up in the postseason, he'd love to show Buffalo what it's missing.

"I wouldn't say it was painful," Taylor said of being dealt by the Bills. "I have nothing to hold (hang) my head about in my time in Buffalo. It was a progression from a players' standpoint each and every year, but of course why would I not want to beat that team in the playoffs if it comes down to that?

"I'm always excited to compete. But I know those guys, played against those guys, the majority of those guys for the past three years, some new players and I'd love to play against those guys."

It didn't take long for the 29-year-old Taylor to ingratiate himself to the Browns. He has set an example on and off the field, whether arriving at 5 a.m. to get in an early morning workout or staying late to break down film.

It's the only way Taylor knows, and he's having a strong influence on rookie Baker Mayfield, the No. 1 overall pick who will one day supplant him as Cleveland's starter.

Mayfield said Taylor is showing him how to be a professional.

"Just the work ethic and everything he brings to the table every day," Mayfield said, when asked about Taylor's standards. "It's the same every day. You hear (offensive coordinator) coach (Todd) Haley talk about 'not being a yo-yo guy. You want to be consistent,' and Ty really, really is the example of that.

"He's the same guy every day. You know exactly what you're going to get out of him, and that's important for our guys to see that. They see the standard. They see the expectations, and he lives up to it every day."

Taylor set a high bar for himself last week by recording a perfect 158.3 rating in two series against the New York Giants. He completed 5 of 5 passes for 99 yards and a touchdown before turning the offense over to Mayfield, who shined in his NFL preseason debut.

Mayfield's performance prompted a push — locally and nationally — for the Browns to start the Heisman Trophy winner over Taylor.

But while there's noise outside the Browns, Taylor's world is tranquil.

"I really don't hear those comments," he said. "I've always been focused on myself. Like I said from Day One, I'm in competition with myself and how can I make myself better each and every day and I'm going to keep having that mindset and push myself to be the best player I can be."

NOTES: Tempers flared during practice, which featured three fights, including one involving Pro Bowl WR Jarvis Landry and starting CB Terrence Mitchell. As Landry rolled on the ground following a catch, Mitchell went over the top of him and hit the receiver's back. Landry popped up and slammed the ball of Mitchell's helmet before they grabbed each other's facemasks. Coach Hue Jackson chalked the skirmishes up to the dog days of camp. "This is football. We have been going after it," Jackson said. "It is not something that we want. We are men. Guys know as long as we do not start swinging with our fists and we let it go, we can move on from it." ... Former Ohio State DT Jonathan Hankins is scheduled to work out for the Browns on Wednesday. He previously played for the Giants and Colts.